In previous work, we have demonstrated the perfect integration on silicon of micrometric GaAs crystals without any structural defects nor stress, using Epitaxal Lateral Overgrowth on Tunnel Oxide from nanoseeds (ELTOn). Then, it would be very interesting to integrate the crystals in a regular way to have a quasi-complete covering of the Si substrate, without coalescence of the GaAs microcrystals to maintain their very good electronic properties, avoiding then detrimental grain boundaries. The main focus of this work is to address the issue of the doping determination in a single micrometric size GaAs crystal which is a pre-requisite to develop the future design and technology of multijunction solar cells based on an array of non-coalescent GaAs crystals free of structural defects. In a previous work, local electrical characterizations by CP-AFM revealed a rather high non intentional ptype doping. To obtain a quantitative estimation of the doping level, we propose a contactless method based on the photoluminescence measurement of the evolution of the bandgap versus temperature and its modeling.